DISTILLATION DESIGN AND CONTROL...

DISTILLATION DESIGNAND CONTROL USINGASPENTM SIMULATION

WILLIAM L. LUYBEN

Lehigh UniversityBethlehem, Pennsylvania

A JOHN WILEY & SONS, INC., PUBLICATION

Innodata0471785245.jpg


WILLIAM L. LUYBEN

Lehigh UniversityBethlehem, Pennsylvania

A JOHN WILEY & SONS, INC., PUBLICATION

Copyright # 2006 by John Wiley & Sons, Inc. All rights reserved.

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Library of Congress Cataloging-in-Publication Data:

Luyben, William L.

Distillation design and control using Aspen simulation / William L.

Luyben.

p. cm.

Includes index.

ISBN-13: 978-0-471-77888-2 (cloth)

ISBN-10: 0-471-77888-5 (cloth)

1. Distillation apparatusDesign and construction. 2. Chemical

process controlSimulation methods. I. Title.

TP159.D5L89 2006

6600.28425- -dc222005023397

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

http://www.copyright.comhttp://www.wiley.com/go/permissionhttp://www.wiley.com

Dedicated to the memory of the pioneers of

Lehigh Chemical Engineering:

Alan Foust, Len Wenzel, and Curt Clump

CONTENTS

PREFACE xi

1 FUNDAMENTALS OF VAPORLIQUID PHASEEQUILIBRIUM (VLE) 1

1.1 Vapor Pressure / 1

1.2 Binary VLE Phase Diagrams / 3

1.3 Physical Property Methods / 7

1.4 Relative Volatility / 7

1.5 Bubblepoint Calculations / 9

1.6 Ternary Diagrams / 10

1.7 VLE Nonideality / 12

1.8 Residue Curves for Ternary Systems / 18

1.9 Conclusion / 26

2 ANALYSIS OF DISTILLATION COLUMNS 27

2.1 Design Degrees of Freedom / 27

2.2 Binary MCCabeThiele Method / 28

2.3 Approximate Multicomponent Methods / 38

2.4 Analysis of Ternary Systems Using DISTIL / 41

2.5 Conclusion / 44

vii

3 SETTING UP A STEADY-STATE SIMULATION 45

3.1 Configuring a New Simulation / 45

3.2 Specifying Chemical Components and Physical Properties / 53

3.3 Specifying Stream Properties / 58

3.4 Specifying Equipment Parameters / 60

3.5 Running the Simulation / 64

3.6 Using Design Spec/Vary Function / 66

3.7 Finding the Optimum Feed Tray and Minimum Conditions / 80

3.8 Column Sizing / 81

3.9 Conclusion / 84

4 DISTILLATION ECONOMIC OPTIMIZATION 85

4.1 Heuristic Optimization / 85

4.2 Economic Basis / 87

4.3 Results / 89

4.4 Operating Optimization / 91

4.5 Conclusion / 97

5 MORE COMPLEX DISTILLATION SYSTEMS 98

5.1 Methyl Acetate/Methanol/Water System / 98

5.2 Ethanol Dehydration / 112

5.3 Heat-Integrated Columns / 122

5.4 Conclusion / 129

6 STEADY-STATE CALCULATIONS FOR CONTROLSTRUCTURE SELECTION 130

6.1 Summary of Methods / 131

6.2 Binary Propane/Isobutane System / 133

6.3 Ternary BTX System / 137

6.4 Multicomponent Hydrocarbon System / 141

6.5 Ternary Azeotropic System / 145


7 CONVERTING FROM STEADY STATE TODYNAMIC SIMULATION 151

7.1 Equipment Sizing / 151

7.2 Exporting to Aspen Dynamics / 153

7.3 Opening the Dynamic Simulation in Aspen Dynamics / 156

7.4 Installing Basic Controllers / 158

7.5 Installing Temperature and Composition Controllers / 166

viii CONTENTS

7.6 Performance Evaluation / 179

7.7 Comparison with Economic Optimum Design / 184


8 CONTROL OF MORE COMPLEX COLUMNS 188

8.1 Methyl Acetate Column / 188

8.2 Columns with Partial Condensers / 190

8.3 Control of Heat-Integrated Distillation Columns / 209

8.4 Control of Azeotropic Columns/Decanter System / 222


9 REACTIVE DISTILLATION 232

9.1 Introduction / 232

9.2 Types of Reactive Distillation Systems / 234

9.3 TAME Process Basics / 238

9.4 TAME Reaction Kinetics and VLE / 241

9.5 Plantwide Control Structure / 246


10 CONTROL OF SIDESTREAM COLUMNS 251

10.1 Liquid Sidestream Column / 252

10.2 Vapor Sidestream Column / 257

10.3 Liquid Sidestream Column with Stripper / 264

10.4 Vapor Sidestream Column with Rectifier / 271

10.5 Sidestream Purge Column / 281


11 CONTROL OF PETROLEUM FRACTIONATORS 291

11.1 Petroleum Fractions / 292

11.2 Characterization of Crude Oil / 296

11.3 Steady-State Design of PREFLASH Column / 304

11.4 Control of PREFLASH Column / 311

11.5 Steady-State Design of Pipestill / 316

11.6 Control of Pipestill / 333


INDEX 343

CONTENTS ix

PREFACE

The rapid increase in the price of crude oil in recent years (as of 2005) and the resulting

sticker shock at the gas pump have caused the scientific and engineering communities

to finally understand that it is time for some reality checks on our priorities. Energy

is the real problem that faces the world, and it will not be solved by the recent fads of

biotechnology or nanotechnology. Energy consumption is the main producer of carbon

dioxide, so it is directly linked with the problem of global warming.

A complete reassessment of our energy supply and consumption systems is required.

Our terribly inefficient use of energy in all aspects of our modern society must be

halted. We waste energy in our transportation system with poor-mileage SUVs and

inadequate railroad systems. We waste energy in our water systems by using energy to

produce potable water, and then flush most of it down the toilet. This loads up our

waste disposal plants, which consume more energy. We waste energy in our food

supply system by requiring large amounts of energy for fertilizer, herbicides, pesticides,

tillage, and transporting and packaging our food for consumer convenience. The old

farmers markets provided better food at lower cost and required much less energy.

One of the most important technologies in our energy supply system is distillation.

Essentially all our transportation fuel goes through at least one distillation column on

its way from crude oil to the gasoline pump. Large distillation columns called pipestills

separate the crude into various petroleum fractions based on boiling points. Intermediate

fractions go directly to gasoline. Heavy fractions are catalytically or thermally cracked

to form more gasoline. Light fractions are combined to form more gasoline. Distillation is

used in all of these operations.

Even when we begin to switch to renewable sources of energy such as biomass, the

most likely transportation fuel will be methanol. The most likely process is the partial

oxidation of biomass to produce synthesis gas (a mixture of hydrogen, carbon monoxide,

and carbon dioxide) and the subsequent reaction of these components to produce methanol

and water. Distillation to separate methanol from water is an important part of this process.

Distillation is also used to produce the oxygen used in the partial oxidation reactor.

Therefore distillation is, and will remain in the twenty-first century, the premier

separation method in the chemical and petroleum industries. Its importance is

xi

unquestionable in helping to provide food, heat, shelter, clothing, and transportation in our

modern society. It is involved in supplying much of our energy needs. The distillation

columns in operation around the world number in the tens of thousands.

The analysis, design, operation, control, and optimization of distillation columns

have been extensively studied for almost a century. Until the advent of computers, hand

calculations and graphical methods were developed and widely applied in these studies.

Since about 1950, analog and digital computer simulations have been used to solve

many engineering problems. Distillation analysis involves iterative vaporliquid phase

equilibrium calculations and tray-to-tray component balances that are ideal for digital

computation.

Initially most engineers wrote their own programs to solve both the nonlinear

algebraic equations that describe the steady-state operation of a distillation column and

the nonlinear ordinary differential equations that describe its dynamic behavior. Many

chemical and petroleum companies developed their own in-house steady-state process

simulation programs in which distillation was an important unit operation. Commercial

steady-state simulators took over around the mid-1980s and now dominate the field.

Commercial dynamic simulators were developed quite a bit later. They had to wait

for advancements in computer technology to provide the very fast computers required.

The current state of the art is that both steady-state and dynamic simulations of distillation

columns are widely used in industry and in universities.

My own technical experience has pretty much followed this history of distillation

simulation. My practical experience started back in a high-school chemistry class in

which we performed batch distillations. Next came an exposure to some distillation

theory and running a pilot-scale batch distillation column as an undergraduate at Penn

State, learning from Arthur Rose and Black Mike Cannon. Then there were 5 years

of industrial experience in Exxon refineries as a technical service engineer on pipestills,

vacuum columns, light-end units, and alkylation units, all of which used distillation

extensively.

During this period the only use of computers that I was aware of was for solving linear

programming problems associated with refinery planning and scheduling. It was not until

returning to graduate school in 1960 that I personally started to use analog and digital

computers. Bob Pigford taught us how to program a Bendix G12 digital computer,

which used paper tape and had such limited memory that programs were severely

restricted in length and memory requirements. Dave Lamb taught us analog simulation.

Jack Gerster taught us distillation practice.

Next there were 4 years working in the Engineering Department of DuPont on process

control problems, many of which involved distillation columns. Both analog and digital

simulations were heavily used. A wealth of knowledge was available from a stable of

outstanding engineers: Page Buckley, Joe Coughlin, J. B. Jones, Neal OBrien, and

Tom Keane, to mention only a few.

Finally, there have been over 35 years of teaching and research at Lehigh in which

many undergraduate and graduate students have used simulations of distillation

columns in isolation and in plantwide environments to learn basic distillation principles

and to develop effective control structures for a variety of distillation column configur-

ations. Both homegrown and commercial simulators have been used in graduate research

and in the undergraduate senior design course.

The purpose of this book is to try to capture some of this extensive experience with

distillation design and control so that it is available to students and young engineers

xii PREFACE

when they face problems with distillation columns. This book covers much more than just

the mechanics of using a simulator. It uses simulation to guide in developing the optimum

economic steady-state design of distillation systems, using simple and practical

approaches. Then it uses simulation to develop effective control structures for dynamic

control. Questions are addressed as to whether to use single-end control or dual-

composition control, where to locate temperature control trays, and how excess degrees

of freedom should be fixed.

There is no claim that the material is all new. The steady-state methods are discussed

in most design textbooks. Most of the dynamic material is scattered around in a number

of papers and books. What is claimed is that this book pulls this material together in a

coordinated, easily accessible way. Another unique feature is the combination of design

and control of distillation columns in a single book.

There are three steps in developing a process design. The first is conceptual design, in

which simple approximate methods are used to develop a preliminary flowsheet. This step

for distillation systems is covered very thoroughly in another textbook.1 The next step

is preliminary design, in which rigorous simulation methods are used to evaluate both

steady-state and dynamic performance of the proposed flowsheet. The final step is

detailed design, in which the hardware is specified in great detail, with specifics such

as types of trays, number of sieve tray holes, feed and reflux piping, pumps, heat exchanger

areas, and valve sizes. This book deals with the second stage, preliminary design.

The subject of distillation simulation is a very broad one, which would require many

volumes to cover comprehensively. The resulting encyclopedia-like books would be too

formidable for a beginning engineer to try to tackle. Therefore this book is restricted in

its scope to only those aspects that I have found to be the most fundamental and the

most useful. Only continuous distillation columns are considered. The area of batch

distillation is very extensive and should be dealt with in another book. Only staged

columns are considered. They have been successfully applied for many years. Rate-

based models are fundamentally more rigorous, but they require that more parameters

be known or estimated.

Only rigorous simulations are used in this book. The book by Doherty and Malone is

highly recommended for a detailed coverage of approximate methods for conceptual

steady-state design of distillation systems.

I hope that the reader finds this book useful and readable. It is a labor of love that

is aimed at taking some of the mystery and magic out of designing and operating a

distillation column.

WILLIAM L. LUYBEN

1M. F. Doherty and M. F. Malone, Conceptual Design of Distillation Systems, McGraw-Hill, 2001.

PREFACE xiii

CHAPTER 1

FUNDAMENTALS OF VAPORLIQUIDPHASE EQUILIBRIUM (VLE)

Distillation occupies a very important position in chemical engineering. Distillation and

chemical reactors represent the backbone of what distinguishes chemical engineering

from other engineering disciplines. Operations involving heat transfer and fluid mechanics

are common to several disciplines. But distillation is uniquely under the purview of chemi-

cal engineers.

The basis of distillation is phase equilibrium, specifically, vaporliquid (phase) equili-

brium (VLE) and in some cases vaporliquidliquid (phase) equilibrium (VLLE). Distil-

lation can effect a separation among chemical components only if the compositions of the

vapor and liquid phases that are in phase equilibrium with each other are different. A

reasonable understanding of VLE is essential for the analysis, design, and control of

distillation columns.

The fundamentals of VLE are briefly reviewed in this chapter.

1.1 VAPOR PRESSURE

Vapor pressure is a physical property of a pure chemical component. It is the pressure that

a pure component exerts at a given temperature when both liquid and vapor phases are

present. Laboratory vapor pressure data, usually generated by chemists, are available

for most of the chemical components of importance in industry.

Vapor pressure depends only on temperature. It does not depend on composition

because it is a pure component property. This dependence is normally a strong one with

an exponential increase in vapor pressure with increasing temperature. Figure 1.1 gives

two typical vapor pressure curves, one for benzene and one for toluene. The natural log

of the vapor pressures of the two components are plotted against the reciprocal of the

1

Distillation Design and Control Using AspenTM Simulation, By William L. LuybenCopyright # 2006 John Wiley & Sons, Inc.

absolute temperature. As temperature increases, we move to the left in the figure, which

means a higher vapor pressure. In this particular figure, the vapor pressure PS of each com-

ponent is given in units of millimeters of mercury (mmHg). The temperature is given in

Kelvin units.

Looking at a vertical constant-temperature line shows that benzene has a higher vapor

pressure than does toluene at a given temperature. Therefore benzene is the lighter com-

ponent from the standpoint of volatility (not density). Looking at a constant-pressure hori-

zontal line shows that benzene boils at a lower temperature than does toluene. Therefore

benzene is the lower boiling component. Note that the vapor pressure lines for benzene

and toluene are fairly parallel. This means that the ratio of the vapor pressures does not

change much with temperature (or pressure). As discussed in a later section, this means

that the ease or difficulty of the benzene/toluene separation (the energy required tomake a specified separation) does not change much with the operating pressure of the

column. Other chemical components can have temperature dependences that are quite

different.

If we have a vessel containing a mixture of these two components with liquid and vapor

phases present, the concentration of benzene in the vapor phase will be higher than that in

the liquid phase. The reverse is true for the heavier, higher-boiling toluene. Therefore

benzene and toluene can be separated in a distillation column into an overhead distillate

stream that is fairly pure benzene and a bottoms stream that is fairly pure toluene.

Equations can be fitted to the experimental vapor pressure data for each component

using two, three, or more parameters. For example, the two-parameter version is

lnPSj Cj Dj=T

The Cj and Dj are constants for each pure chemical component. Their numerical values

depend on the units used for vapor pressure [mmHg, kPa, psia (pounds per square inch

absolute), atm, etc.] and on the units used for temperature (K or 8R).

1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.43

4

5

6

7

8

9

10

11

12

ln P

S(w

ith

PS

in m

m H

g)

Reciprocal of Absolute Temperature -1000/T (with T in K)

Benzene

Toluene

Increasing Temperature

Figure 1.1 Vapor pressures of pure benzene and toluene.

2 FUNDAMENTALS OF VAPORLIQUID PHASE EQUILIBRIUM

1.2 BINARY VLE PHASE DIAGRAMS

Two types of vaporliquid equilibrium diagrams are widely used to represent data for

two-component (binary) systems. The first is a temperature versus x and y diagram

(Txy). The x term represents the liquid composition, usually expressed in terms of mole

fraction. The y term represents the vapor composition. The second diagram is a plot of

x versus y.

These types of diagrams are generated at a constant pressure. Since the pressure in a

distillation column is relatively constant in most columns (the exception is vacuum distil-

lation, in which the pressures at the top and bottom are significantly different in terms of

absolute pressure level), a Txy diagram, and an xy diagram are convenient for the analysis

of binary distillation systems.

Figure 1.2 gives the Txy diagram for the benzene/toluene system at a pressure of 1 atm.The abscissa shows the mole fraction of benzene; the ordinate, temperature. The lower

curve is the saturated liquid line, which gives the mole fraction of benzene in the

liquid phase x. The upper curve is the saturated vapor line, which gives the mole fraction

of benzene in the vapor phase y. Drawing a horizontal line at some temperature and

reading off the intersection of this line with the two curves give the compositions of the

two phases. For example, at 370 K the value of x is 0.375 mole fraction benzene and

the value of y is 0.586 mole fraction benzene. As expected, the vapor is richer in the

lighter component.

At the leftmost point we have pure toluene (0 mole fraction benzene), so the boiling

point of toluene at 1 atm can be read from the diagram (384.7 K). At the rightmost

point we have pure benzene (1 mole fraction benzene), so the boiling point of benzene

at 1 atm can be read from the diagram (353.0 K). In the region between the curves,

there are two phases; in the region above the saturated vapor curve, there is only a

single superheated vapor phase; in the region below the saturated liquid curve, there

is only a single subcooled liquid phase.

Figure 1.2 Txy diagram for benzene and toluene at 1 atm.

1.2 BINARY VLE PHASE DIAGRAMS 3

The diagram is easily generated in Aspen Plus by going to Tools on the upper toolbar

and selecting Analysis, Property, and Binary. The window shown in Figure 1.3 opens and

specifies the type of diagram and the pressure. Then we click the Go button.

The pressure in the Txy diagram given in Figure 1.2 is 1 atm. Results at several press-

ures can also be generated as illustrated in Figure 1.4. The higher the pressure, the higher

the temperatures.

Figure 1.3 Specifying Txy diagram parameters.

Figure 1.4 Txy diagrams at two pressures.


Figure 1.5 Using Plot Wizard to generate xy diagram.

Figure 1.6 Using Plot Wizard to generate xy diagram.

1.2 BINARY VLE PHASE DIAGRAMS 5

The other type of diagram, an xy diagram, is generated in Aspen Plus by clicking the

Plot Wizard button at the bottom of the Binary Analysis Results window that also opens

when the Go button is clicked to generate the Txy diagram. As shown in Figure 1.5,

this window also gives a table of detailed information. The window shown in

Figure 1.6 opens, and YX picture is selected. Clicking the Next and Finish buttons gener-

ates the xy diagram shown in Figure 1.7.

Figure 1.7 xy diagram for benzene/toluene.

Figure 1.8 xy diagram for propylene/propane.


Figure 1.8 gives an xy diagram for the propylene/propane system. These componentshave boiling points that are quite close, which leads to a very difficult separation.

These diagrams provide valuable insight into the VLE of binary systems. They can be

used for quantitative analysis of distillation columns, as we will demonstrate in Chapter

2. Three-component ternary systems can also be represented graphically, as discussed

in Section 1.6.

1.3 PHYSICAL PROPERTY METHODS

The observant reader may have noticed in Figure 1.3 that the physical property method

specified for the VLE calculations in the benzene/toluene example was ChaoSeader. This method works well for most hydrocarbon systems.

One of the most important issues involved in distillation calculations is the selection of

an appropriate physical property method that will accurately describe the phase equili-

brium of the chemical component system. The Aspen Plus library has a large number

of alternative methods. Some of the most commonly used methods are ChaoSeader,

van Laar, Wilson, Unifac, and NRTL.

In most design situations there is some type of data that can be used to select the most

appropriate physical property method. Often VLE data can be found in the literature. The

multivolume DECHEMA data books1 provide an extensive source of data.

If operating data from a laboratory, pilot plant, or plant column are available, they can

be used to determine what physical property method fits the column data. There could be a

problem in using column data in that the tray efficiency is also unknown and the VLE

parameters cannot be decoupled from the efficiency.

1.4 RELATIVE VOLATILITY

One of the most useful ways to represent VLE data is by employing relative volatility,

which is the ratio of the y/x values [vapor mole fraction over (divided by) liquid mole frac-tion] of two components. For example, the relative volatility of component L with respect

to component H is defined in the following equation:

aLH ;yL=xLyH=xH

The larger the relative volatility, the easier the separation.

Relative volatilities can be applied to both binary and multicomponent systems. In the

binary case, the relative volatility a between the light and heavy components can be usedto give a simple relationship between the composition of the liquid phase (x is the mole

fraction of the light component in the liquid phase) and the composition of the vapor

phase ( y is the mole fraction of the light component in the vapor phase):

y ax1 (a 1)x

1J. Gmehling et al., Vapor-Liquid Equilibrium Data Collection, DECHEMA, Frankfurt/Main, 1993.

1.4 RELATIVE VOLATILITY 7

Figure 1.9 gives xy curves for several values of a, assuming that a is constant over theentire composition space.

In the multicomponent case, a similar relationship can be derived. Suppose that there

are NC components. Component 1 is the lightest, component 2 is the next lightest, and

so forth down to the heaviest of all the components, component H. We define the relative

volatility of component j with respect to component H as aj:

aj yj=xjyH=xH

Solving for yj and summing all the y values (which must add to unity) give

yj ajxj yHxH

XNCj1

yj 1 XNCj1

ajxjyH

xH

1 yHxH

XNCj1

ajxj

Then, solving for yH/xH and substituting this into the first equation above give

yH

xH 1PNC

j1 ajxj

yj ajxjPNCj1 ajxj

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Liquid composition (mole fraction light)

Vap

or c

ompo

sitio

n (m

ole

frac

tion

light

)

5=

2=

3.1=

Figure 1.9 xy curves for relative volatilities of 1.3, 2, and 5.


The last equation relates the vapor composition to the liquid composition for a constant

relative volatility multicomponent system. Of course, if relative volatilities are not con-

stant, this equation cannot be used. What is required is a bubblepoint calculation,

which is discussed in the next section.

1.5 BUBBLEPOINT CALCULATIONS

The most common VLE problem is to calculate the temperature and vapor composition yjthat is in equilibrium with a liquid at a known total pressure of the system P and with a

known liquid composition (all the xj values). At phase equilibrium the chemical poten-

tial mj of each component in the liquid and vapor phases must be equal:

mLj mVj

The liquid-phase chemical potential of component j can be expressed in terms of liquid

mole fraction xj, vapor pressure PjS, and activity coefficient gj:

mLj xjPSj gj

The vapor-phase chemical potential of component j can be expressed in terms of vapor

mole fraction yj, the total system pressure P, and fugacity coefficient sj:

mVj yjPsj

Therefore the general relationship between vapor and liquid phases is

yjPsj xjPSj gj

If the pressure of the system is not high, the fugacity coefficient is unity. If the liquid phase

is ideal (i.e., there is no interaction between the molecules), the activity coefficient is

unity. The latter situation is much less common than the former because components inter-

act in liquid mixtures. They can either attract or repulse. Section 1.7 discusses nonideal

systems in more detail.

Let us assume that the liquid and vapor phases are both ideal (gj 1 and sj 1). In thissituation the bubblepoint calculation involves an iterative calculation to find the tempera-

ture T that satisfies the equation

P XNCj1

xjPSj(T)

The total pressure P and all the xj values are known. In addition, equations for the vapor

pressures of all components as functions of temperature T are known. The Newton

Raphson convergence method is convenient and efficient in this iterative calculation

because an analytical derivative of the temperature-dependent vapor pressure functions

PS can be used.

1.5 BUBBLEPOINT CALCULATIONS 9

1.6 TERNARY DIAGRAMS

Three-component systems can be represented in two-dimensional ternary diagrams. There

are three components, but the sum of the mole fractions must add to unity. Therefore, spe-

cifying two mole fractions completely defines the composition.

A typical rectangular ternary diagram is given in Figure 1.10. The mole fraction of

component 1 is shown on the abscissa; the mole fraction of component 2, on the ordinate.

Both of these dimensions run from 0 to 1. The three corners of the triangle represent the

three pure components.

Since only two compositions define the composition of a stream, the stream can be

located on this diagram by entering the appropriate coordinates. For example,

Figure 1.10 shows the location of stream F that is a ternary mixture of 20 mol%

n-butane (C4), 50 mol% n-pentane (C5), and 30 mol% n-hexane (C6).

One of the most useful and interesting aspects of ternary diagrams is the ternary

mixing rule, which states that if two ternary streams are mixed together (one is stream

D with composition xD1 and xD2 and the other is stream B with composition xB1 and

xB2), the mixture has a composition (z1 and z2) that lies on a straight line in a x1x2ternary diagram that connects the xD and xB points.

Figure 1.11 illustrates the application of this mixing rule to a distillation column. Of

course, a column separates instead of mixes, but the geometry is exactly the same. The

two products D and B have compositions located at point (xD1xD2) and (xB1xB2),

respectively. The feed F has a composition located at point (z1z2) that lies on a straight

line joining D and B.

This geometric relationship is derived from the overall molar balance and the two

overall component balances around the column:

F D BFz1 DxD1 BxB1Fz2 DxD2 BxB2

Feed composition:

zC4 = 0.2 and zC5 = 0.5

C4

C5

F

o0.2

0.5C6 00

1

1

Figure 1.10 Ternary diagram.


Substituting the first equation in the second and third gives

(D B)z1 DxD1 BxB1(D B)z2 DxD2 BxB2

Rearranging these two equations to solve for the ratio of B over D gives

D

B z1 xD1

xB1 z1D

B z2 xD2

xB2 z2

Equating these two equations and rearranging give

z1 xD1xB1 z1

z2 xD2xB2 z2

xD1 z1z2 xD2

z1 xB1xB2 z2

Figure 1.12 shows how the ratios given above can be defined in terms of the tangents of the

angles u1 and u2. The conclusion is that both angles must be equal, so the line between Dand B must pass through F.

As we will see in subsequent chapters, this straight-line relationship is quite useful in

representing what is going on in a ternary distillation system.

C4Butane

60 psia

C4C5C6

C4

C5

o

FD

o

o

C5C6

B

F

B

D

xD,C5 = 0.05

xD,C6 0

xB,C4 = 0.05xB,C5 = ?

Overall component-balance line

Figure 1.11 Ternary mixing rule.

1.6 TERNARY DIAGRAMS 11

1.7 VLE NONIDEALITY

Liquid-phase ideality (activity coefficients gj 1) occurs only when the components arequite similar. The benzene/toluene system is a common example. As shown in the sixthand seventh columns in Figure 1.5, the activity coefficients of both benzene and toluene

are very close to unity.

However, if components are dissimilar, nonideal behavior occurs. Consider a mixture

of methanol and water. Water is very polar. Methanol is polar on the OH end of the mol-

ecule, but the CH3 end is nonpolar. This results in some nonideality. Figure 1.13a gives the

xy curve at 1 atm. Figure 1.13b gives a table showing how the activity coefficients of the

two components vary over composition space. The Unifac physical property method is

used. The g values range up to 2.3 for methanol at the x 0 limit and 1.66 for water atx 1. A plot of the activity coefficients can be generated by selecting the Gammapicture when using the Plot Wizard. The resulting plot is given in Figure 1.13c.

Now consider a mixture of ethanol and water. The CH3CH2 end of the ethanol mol-

ecule is more nonpolar than the CH3 end of methanol. We would expect the nonideality to

be more pronounced, which is exactly what the Txy diagram, the activity coefficient

results, and the xy diagram given in Figure 1.14 show.

Note that the activity coefficient of ethanol at the x 0 end (pure water) is very large(gEtOH 6.75) and also that the xy curve shown in Figure 1.14c crosses the 458 line(x y) at 90 mol% ethanol. This indicates the presence of an azeotrope. Note alsothat the temperature at the azeotrope (351.0 K) is lower than the boiling point of

ethanol (351.5 K).

An azeotrope is defined as a composition at which the liquid and vapor compositions

are equal. Obviously, when this occurs, there can be no change in the liquid and vapor

compositions from tray to tray in a distillation column. Therefore an azeotrope represents

a distillation boundary.

Azeotropes occur in binary, ternary, and multicomponent systems. They can be

homogeneous (single liquid phase) or heterogeneous (two liquid phases). They can

be minimum boiling or maximum boiling. The ethanol/water azeotrope is aminimum-boiling homogeneous azeotrope.

o

o

oxD1

xD2 xB2

xB1

z1

z2

D

B

F

tan q2

tan q1

xB2 z2

z1 xB1

z2 xD2

xD1 z1

1

2

Figure 1.12 Proof of collinearity.


The software Aspen Split provides a convenient method for calculating azeotropes. Go

to Tools on the top toolbar, then select Aspen Split and Azeotropic Search. The window

shown at the top of Figure 1.15 opens, on which the components and pressure level are

specified. Clicking on Azeotropes opens the window shown at the bottom of Figure 1.15,

which gives the calculated results: a homogeneous azeotrope at 788C (351 K) with compo-sition 89.3 mol% ethanol.

Up to this point we have been using Split as an analysis tool. Aspen Technology plans

to phase out Split in new releases of their Engineering Suite and will offer another tool

called DISTIL, which has more capability. To illustrate some of the features of

DISTIL, let us use it to study a system in which there is more dissimilarity of the molecules

Figure 1.13 (a) Txy diagram for methanol/water; (b) activity coefficients for methanol/water;(c) activity coefficient plot for methanol/water.

1.7 VLE NONIDEALITY 13

by looking at the n-butanol/water system. The normal boiling point of n-butanol is 398 K,while that of water is 373 K, so water is the low boiler in this system.

The DISTIL program is opened in the usual way. Clicking the Managers button on the

top toolbar of the DISTIL window and clicking Fluid Package Manager opens the window

shown at the top of Figure 1.16. Click the Add button. The window shown at the bottom of

Figure 1.16 opens. On the Property Package page tab, the UNIFAC VLE package is

selected with Ideal Gas. Then click the Select button on the right side of the window.

Figure 1.13 Continued.

Figure 1.14 Txy diagram for ethanol/water (a), activity coefficient plot (b), and xy plot (c) forethanol/water.


Date post:	06-Mar-2018
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